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5. (19 pts) Consider the following grammar for simple assignment statements: AssignStmt Var=E id | id [ Index ] Var Index Var|nr|E+EE-EE*EE/E|(E) (a) (12 pts) Build a parse tree for each of the following assignment statements: a [2] = b + 1 x = v[k-3] (b) (7 pts) Rewrite the grammar so that it allows multi-dimensional arrays (instead of just one index, allow a list of indices separated by commas). For instance, each of the following should be a valid string under the new grammar: m[5,3] = x y = p[i+1,j, k-1]